Geodesic
The Structure of Semisimple Symmetric Spaces
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 157-180

Voir la notice de l'article provenant de la source Cambridge University Press

A semisimple symmetric space can be defined as a homogeneous space G/H, where G is a semisimple Lie group, H an open subgroup of the fixed point group of an involutive automorphism of G. These spaces can also be characterized as the affine symmetric spaces or pseudo-Riemannian symmetric spaces or symmetric spaces in the sense of Loos [4] with semisimple automorphism groups [3, 4]. The connected semisimple symmetric spaces are all known: they have been classified by Berger [2] on the basis of Cartan's classification of the Riemannian symmetric spaces. However, the list of these spaces is much too long to make a detailed case by case study feasible. In order to do analysis on semisimple symmetric spaces, for example, one needs a general structure theory, just as in the case of Riemannian symmetric spaces and semisimple Lie groups. 
Rossmann, W. The Structure of Semisimple Symmetric Spaces. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 157-180. doi: 10.4153/CJM-1979-017-6
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